Louis Katz on sat 3 jul 10
As a society we do not credit children with enough. One skill we teach to=
late is a process called dimensional analysis. Once understood it solves
lots of problems and gives clues to the solutions of other problems. It c=
be taught at least in part to elementary school kids.
In order to get SQUARE inches, somewhere you must multiply a length by a =
Formula for the area or square inches of a circle Pi times the radius tim=
The result of multiplying the radius (given in inches) times itself, time=
Pi (just a number it has no unit associated with it) is square inches or
For a rectangular surface you multiply inches* inches giving you inches
squared or square inches.
For a cube, you cube the inches, that is inches x inches x inches .
So a cube is just a square multiplied by its height leading you from squa=
inches to cubic inches.
If you are trying to get from dollars per gallon to baht(Thai currency) p=
liter pricing of gasoline and you know how to use dimensional analysis, t=
conversion becomes trivial. Somehow I neglected to learn dimensional
analysis in High School Electronics from Mr. Gardner. I owe him an apolog=
for wasting his time. He was a good teacher. I should have learned it the=
but it waited to really resonate until college calculus.=3D20
I learned glaze calculation by rote by studying Rhodes. I wrote a compute=
program to do unity to batch conversions on the main frame at the Univers=
of Michigan in 1975. Had I really understood dimensional analysis when I =
first learning glaze calc, I would have understood that the problem is
essentially trivial other than keeping the arithmetic straight . Once the=
fact that all it was was a conversion from mols, to grams was really beat=
into my head, it became easier to do and explain.=3D20
All units in inches
Length =3D3D length in inches
Length X Width =3D3D square inches or inches squared
Length X Width X Height =3D3D cubic inches or inches cubed=3D20
So surface of a cylinder =3D3D Pi X diameter in inches X Height in Inches
2 inch units multiplied gives you square inches
Volume of a Cylinder =3D3D the square inches of one of the ends times the
height. (Visualize cutting the cylinder vertically with a grid maybe, tur=
it into "French" Fries.
Or use Pi (no units) X r(inches) X r(inches) X height (inches). Inches X
Inches X Inches gives you cubic inches.
dollars / (length x width x height) =3D3D price per (/) cubic inch or cost =
unit of volume
Hope this helps convert someone to understanding. Much easier to do in p=
The choir has heard it before.
Dannon Rhudy on mon 5 jul 10
Very neat, Louis. Thanks - a highly visible
explication. Should help lots of folks.
As a society we do not credit children with enough. One skill we teach too
late is a process called dimensional analysis. ..........
In order to get SQUARE inches, somewhere you must multiply a length by a
Formula for the area or square inches of a circle Pi times the radius times